Accessibility of optima in pure exchange economies

Assuming differentiable monotonicity and differentiable convexity of utility functions, we show that if y and z are allocations of a pure exchange economy with z optimal and preferred to y by every agent, then there is a trade curve of finite length from y to z. We make no assumption on utility functions designed to ‘keep away from the boundary’. The conclusion need not hold if z is not optimal, unless a special boundary condition is assumed and (l, m) ≠ (2, 2).     

An equivalence of secure implementability and full implementability in truthful strategies in pure exchange economies with Leontief utility functions

This paper investigates the relationship between secure implementability (Saijo et al. in Theor Econ 2:203–229, 2007) and full implementability in truthful strategies (Nicolò in Rev Econ Des 8:373–382, 2004). Although secure implementability is in general stronger than full implementability in truthful strategies, this paper shows that both properties are equivalent under the social choice function that satisfies non-wastefulness (Li and Xue in Econ Theory, doi:10.1007/s00199-012-0724-0) in pure exchange economies with Leontief utility functions.     

Inference ony>y o by using a correlated variable: A three decision approach

Summary In an extension of the two decision approach [Bauer, Scheiber andWohlzogen, 1975] a Bayes solution is aimed at for the three decisiony>y _o,yy _o or no classification on the basic of the measurement of a positively correlated random variableX, which can be measured more easily and/or with smaller expense. Assuming a bivariate normal distribution forX andY optimal decision regions for the measuredx are derived in the case of constant or exponentially increasing losses.

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Zusammenfassung In Erweiterung des Zwei-Entscheidungsproblems [Bauer, Scheiber undWohlzogen, 1975] wird eine Bayes-Lösung für die drei Entscheidungeny>y ₀,yy ₀ oder keine Zuordnung aufgrund der Messung einer mitY positiv korrelierten, einfacher und/oder billiger zugänglichen ZufallsvariablenX angestrebt. Optimale Entscheidungsbereiche für die Messungenx werden bei Voraussetzung einer bivariaten Normalverteilung fürX undY unter der Annahme konstanter oder exponentiell wachsender Verluste bestimmt.

     

Zur Entscheidung y>y0 aufgrund der Messung einer korrelierten Variablen

Zusammenfassung Es wird eine optimale Strategie im Sinne des minimalen erwarteten Verlustes für die beiden Entscheidungeny>y _o undyy _o aufgrund der Messungen einer mitY positiv korrelierten, einfacher und/oder billiger zugänglichen ZufallsvariablenX abgeleitet. Dabei wird angenommen, daßX undY nach einer bivariaten Normalverteilung mit bekannten Parametern verteilt sind und die Entscheidungyy _o getroffen wird, wennx größer ist als ein zu bestimmendesx _o, und die Entscheidungy>y _o, wennx gleich oder kleiner als diesesx _o ist. Für die Bestimmung des optimalenx _o werden zunächst die Kosten für die beiden Fehlentscheidungen jeweils als konstant vorausgesetzt, in einem weiteren Ansatz wird jedoch für die Mißklassifikationyy _o eine mity exponentiell wachsende Risikofunktion angenommen. Um die relative Häufigkeit der zu erwartenden Fehlklassifikationen abschätzen zu können, wird schließlich die bedingte WahrscheinlichkeitP(x>x _o,y) errechnet.

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Summary An optimal strategy, with minimum expected risk, for the decisionsy>y _o oryy _o is constructed on the basis of the measurement of a variableX, which is positively correlated withY and can be measured more easily and/or with smaller expense. A bivariate normal distribution with known parameters is assumed forX andY. For the observationsx a limitx _o is aimed at, so that the decisionsy>y _o oryy _o are taken ifx>x orxx _o respectively. Optimal values ofx _o are first calculated under the assumption of constant losses for the two misclassifications (x>x _o ifyy _o andxx _o ify>y _o). In a further approach the loss for a wrong decisionyy _o is assumed to increase exponentially withy. Finally the conditional probabilityP (x>x _o\y) is calculated to get an assessment of the relative frequencies of wrong decisions to be expected.

     

Über eine Variante der empirischen Verteilungsfunktion

Summary If ₁, ₂,..., _n and ₁, ₂,..., _–1 are two ordered samples from a population with continuous distribution functionF(x), then the points ( _r ,r/n),r=1, 2,..., n–1 provide a better approximation ofF(x) than the points ( _r ,r/n),r=1, 2,..., n, in the following sense:A maximal upper deviation and a maximal lower deviation of more theny have — contrary to the points ( _r ,r/n) — equal probability for anyy0, if we deal with the points ( _r ,r/n). This probability is at least for ally in the interval , 1 less than the probability for a maximal upper deviation of more thany in the case of the points ( _r ,r/n). This is shown by a comparison of the Smirnow-Birnbaum-Tingey — formula with an analogous formula for the maximal one-sided deviations of the points( _r ,r/n).     

A numerical representation of semiorders on a countable set

Let be a semiorder on a countable setX and letx⁰ y if and only if either there existsx withxxy or there existsx withxxy. Then ⁰ is a preference relation with transitive indifference, which can be represented by a utility functionf of the usual sort. It is well known that is represented by a pair of real-valued functionsu, v, in the sense thatxy if and only ifu(x)>v(y). We prove that there exists a pair of functionsu, v, representing , such thatu+v is the utility function which represents in the usual sense. Moreover it is easily seen that, for such a pair of functionsu, v, we havex⁰ y if and only if eitheru(x)>u(y) or (u(x)=u(y) andv(x)>v(y)).

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Sommario Consideriamo unsemiordine su un insiemeX numerabile e poniamox⁰ y se e solo se esistex tale chexxy, oppure esistex tale chexxy. In questo caso ⁰ è unordine debole, che può essere rappresentato da una funzione di utilitàf nel senso usuale. D'altra parte è rappresentato da una coppia di funzioniu, v, nel senso chexy se e solo seu(x)>v(y). In questo lavoro si prova che ammette una rappresentazioneu, v tale chex⁰ y se e solo seu(x)+v(x)>u(y)+v(y). Si dimostra altresì che, con riguardo ad una siffatta rappresentazioneu, v di , riescex⁰ y se e solo seu(x)>u(y) oppure (u(x)=u(y) ed anchev(x)>v(y)).

     

Social identity,inequality, and conflict: correction and extension

This paper corrects and extends the analysis in Social Identity, Inequality, and Conflict by James Robinson (Economics of Governance, 2(1), 2001). For conflict along class lines, Robinson finds the total impact of mobility on conflict to be ambiguous. Contrary to his result, I show that, under his assumptions, the effect of social mobility on class conflict is unambiguous. Higher mobility always decreases conflict. In my extension to Robinsons model, I explore mobilitys impact on class conflict in a society where the tax rate is not fixed. I demonstrate that if the tax rate is proportional to the population of the group in power relative to the total population of the society, then the effects of social mobility on class conflict are indeed ambiguous.Submitted: February 2002, Accepted: July 2003,I am grateful to an anonymous referee and Amihai Glazer for their comments. I would also like to thank Herschel Grossman for his help along the way.     

Two-dimensional Bernstein polynomial density estimators

A Bernstein polynomial estimator for f_nN(x, y) for an unknown probability density functionf(x, y) concentrated on the triangle ={(x, y): 0x, y<1,x+y<1} or on the square =(x, y):0 x, y 1 is developed. As a measure of quality the exact order of magnitude for the pointwise mean squared error is established. It is seen that the quality of these Bernstein polynomial estimators is comparable with the quality of the so-called kernel estimators. Further for such estimators uniform weak consistency results and central limit theorems are developed.     

Sensitivity and stability of efficiency classifications in Data Envelopment Analysis

A new technique for assessing the sensitivity and stability of efficiency classifications in Data Envelopment Analysis (DEA) is presented. Here developed for the ratio (CCR) model, this technique extends easily to other DEA variants. An organization's input-outut vector serves as the center for a cell within which the organization's classification remains unchanged under perturbations of the data. For the l ₁, l and generalized l norms, the radius of the maximal cell can be computed using linear programming formulations. This radius can be interpreted as a measure of the classification's stability, especially with respect to errors in the data.Abraham Charnes passed away December 19, 1992.     

Continuous representations of interval orders based on induced preorders

Conditions are given for the existence of a pair of continuous real valued functions (u, v) representing an interval order on a topological space (X, ), in the sense that [xy if and only ifu(x)].I am deeply indepted to Professor Alain Chateauneuf for many valuable suggestions.     

A consistent characteristic function-based test for conditional independence

Y is conditionally independent of Z given X   if Pr{f(y|X,Z)=f(y|X)}=1$\{f(y|X,Z)=f(y|X)\}=1$ for all y on its support, where f(·|·)$f(·|·)$ denotes the conditional density of Y   given (X,Z)$(X,Z)$ or X.$X.$ This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We extend the test of Su and White (2005. A Hellinger-metric nonparametric test for conditional independence. Discussion Paper, Department of Economics, UCSD) in two directions: (1) our test is less sensitive to the choice of bandwidth sequences; (2) our test has power against deviations on the full support of the density of (X,Y,Z$X,Y,Z$). We establish asymptotic normality for our test statistic under weak data dependence conditions. Simulation results suggest that the test is well behaved in finite samples. Applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear Granger causality test fails to detect.     

Nonparametric regression function estimation using interaction least squares splines and comlexity regularization

Let (X, Y) be a pair of random variables withsupp(X)⊆[0,1] ^l andEY ²<∞. Letm ^* be the best approximation of the regression function of (X, Y) by sums of functions of at mostd variables (1≤d≤l). Estimation ofm ^* from i.i.d. data is considered. For the estimation interaction least squares splines, which are defined as sums of polynomial tensor product splines of at mostd variables, are used. The knot sequences of the tensor product splines are chosen equidistant. Complexity regularization is used to choose the number of the knots and the degree of the splines automatically using only the given data. Without any additional condition on the distribution of (X, Y) the weak and strongL ₂-consistency of the estimate is shown. Furthermore, for everyp≥1 and every distribution of (X, Y) withsupp(X)⊆[0,1] ^l ,y bounded andm ^* p-smooth, the integrated squared error of the estimate achieves up to a logarithmic factor the (optimal) rate      

On Bayesian optimum allocation in some two phase sampling problems

Summary For estimating certain parametric functions, we consider the problem of allocatingN _i, the size of the sample from theith population,i=1,2,...,k, at the second phase of sampling of a two phase sampling procedure, given that we taken _i observations from the population at the first phase. We consider that the observations from theith population follow the exponential distribution with mean _i,i=1,2,...,k, and the functions to be estimated are (i) (d_i/_i) and (ii) (d_ii). When the total cost of sampling at the second phase is c _iN_i and is fixed, allocations using the Bayes approach are obtained so that the estimation is as precise as is possible.     

The Perron-Frobenius theorem without additivity

We prove the following non-linear generalization of the Perron-Frobenius theorem. Let A:R^m₊→R^m₊ be continuous, homogeneous of degree 1 and primitive (i.e., for some integer l, x≥yA^lxA^ly); then A has a positive eigenvector x₀, unique up to multiplication by a positive scalar, and for all x0, Aⁿx/|Aⁿx| converges to x₀/|x₀|.     

Sulle polizze vita in regime d'inflazione

In questo lavoro viene postulata e analizzata, in regime d'inflazione, una determinata condizione d'indifferenza per il contraente verso una generica polizza vita.Essa, usata da sola e insieme ad una seconda condizione standard, permette di introdurre due indici di «commerciabilità» per dette polizze, uno relativo e l'altro assoluto.In presence of an inflation ratey>0, the «actual» annual rate of interest, , produced by a generical life assurance policy results lower than the «nominal»,i, fixed on the technical basis but at same time the policy-holder's disinclination for the risk decreases.We consider a determinate indifference condition for the policy-holder to a generical life assurance policy and examine the consequent relations among the variablesi, y and , the revaluation coefficient of the premiums, life annuity funds and insured capitals.In this paper we also introduce two indexes of «marketability» — one of them is relative and the other one is absolute — for a generical life assurance policy in inflation time.     

Characterizations of distributions via linearity of regression of generalized order statistics

Let X (r, n, m, k), 1 r n, denote generalized order statistics based on an absolutely continuous distribution function F. We characterize all distribution functions F for which the following linearity of regression holds E(X(r+l,n,m,k) | X(r,n,m,k))=aX(r,n,m,k)+b.We show that only exponential, Pareto and power distributions satisfy this equation. Using this result one can obtain characterizations of exponential, Pareto and power distributions in terms of sequential order statistics, Pfeifers records and progressive type II censored order statistics. Received July 2001/Revised August 2002     

The cost implications of waste reduction: factor demand, competitiveness and policy implications

Manufacturing produces both good and “bad” outputs, such as waste, which have negative environmental effects. Economic (e.g., tax) and non-economic (e.g., reputation) incentives encourage firms to reduce waste. However, such practices are costly because decreases in output produced or increases in inputs used may accompany waste reduction. We employ a cost function approach to evaluate patterns of output and waste production and capital, labor, and materials use, for UK manufacturing plants. We find that costs of waste reduction generally imply increasing materials use and capital and labor input saving, but vary by county, region, and industry.